Example 2 - A family has two children. What is probability - Examples

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  1. Chapter 13 Class 12 Probability
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Example 2 A family has two children. What is the probability that both the children are boys given that at least one of them is a boy ? A Family has two children Let girls be denoted by ‘g’ & boys be denoted by ‘b’ S = {(g, g), (g, b), (b, g), (b, b)} We need to find the probability that both the children are boys, given at least one them is a boys F : at least one of the children is a boys E : both the children are boys We need to find P(E|F) Also, E ∩ F = {(b, b)} P(E ∩ F ) = 1﷮4﷯ Now, P(E|F) = 𝑃(𝐸 ∩ 𝐹)﷮𝑃(𝐹)﷯ = 1﷮4﷯﷮ 3﷮4﷯﷯ = 1﷮3﷯ ∴ P(E|F) = 𝟏﷮𝟑﷯

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